Competition between charge-density-wave and superconductivity in the kagome metal $\mathrm{Rb}{\mathrm{V}}_3{\mathrm{Sb}}_5$

The interplay between charge-density-wave (CDW) order and superconductivity (SC) in the kagome metal $\mathrm{Rb}{\mathrm{V}}_3{\mathrm{Sb}}_5$ is studied by tracking the evolutions of their transition temperatures $T^{*}$ and $T_{\mathrm{c}}$ as a function of pressure ($P$) via measurements of resistivity and magnetic susceptibility under various hydrostatic pressures up to ∼5 GPa. It is found that the CDW order at $T^{*}$ experiences a subtle modification at $P_{\mathrm{c}1}\approx 1.5\mathrm{GPa}$ before it is completely suppressed around $P_{\mathrm{c}2}\approx 2.4\mathrm{GPa}$. Accordingly, the superconducting transition $T_{\mathrm{c}}\left(P\right)$ exhibits a shallow M-shaped double superconducting dome with two extrema of $T_{\mathrm{c}}^{\mathrm{onset}}\approx 4.4$ and 3.9 K around $P_{\mathrm{c}1}$ and $P_{\mathrm{c}2}$, respectively, leading to a fourfold enhancement of $T_{\mathrm{c}}$ with respect to that at ambient pressure. The constructed $T-P$ phase diagram of $\mathrm{Rb}{\mathrm{V}}_3{\mathrm{Sb}}_5$ resembles that of $\mathrm{Cs}{\mathrm{V}}_3{\mathrm{Sb}}_5$ and shares similar features to many other unconventional superconducting systems with intertwined competing electronic orders. The strong competition between CDW and SC is also evidenced by the broad superconducting transition width in the coexistent region. Our results shed more light on the intriguing physics involving intertwined electronic orders in this topological kagome metal family.

Figure 1

(a) In-plane resistivity ρ($T$) of $\mathrm{Rb}{\mathrm{V}}_3{\mathrm{Sb}}_5$ at ambient pressure from 300 K down to 2 K. The inset shows the $\rho \left(T\right)<1.5\mathrm{K}$, highlighting the superconducting transition. (b) and (c) Field dependences of ρ($H$) measured with field parallel to the $ab$ plane and the $c$ axis at various temperatures. (d) The anisotropic upper critical field ${\mu }_0{H}_{\mathrm{c}2}$, defined as the field at 90% of the normal-state resistivity. (e) The direct current (dc) magnetic susceptibilities under zero-field-cooled (ZFC) and field-cooled (FC) conditions. (f) and (g) Isothermal magnetization at various temperatures with magnetic field parallel to the $ab$ plane and the $c$ axis. (h) The anisotropic lower critical field ${\mu }_0{H}_{\mathrm{c}1}$, defined as the fields at which $M-H$ curves start to deviate from the linear line indicated by the dashed lines in (f) and (g).

Figure 2

Variation of the charge-order-related transition under high pressures. Temperature dependences of (a) resistivity ρ($T$) and (b) its derivative dρ/dT for the $\mathrm{Rb}{\mathrm{V}}_3{\mathrm{Sb}}_5$ sample measured in a piston cylinder cell (PCC) under various pressures up to 2.19 GPa and in a cubic anvil cell (CAC) at 2.4 GPa. The charge-order or charge-density-wave (CDW)-like transition temperature $T^{*}$ are marked by the arrows in the figures. The curves in (a) and (b) have been shifted vertically for clarity.

Figure 3

Variation of the superconducting transition under high pressures in (a) and (b) resistivity and (c) and (d) magnetic susceptibility. The resistivity $\rho \left(T\right)$ data in (a) and (b) are measured up to 2.19 GPa with a piston cylinder cell (PCC) and up to 5.2 GPa with a cubic anvil cell (CAC), respectively. The direct current (dc) magnetization in (c) was recorded in MPMS with a miniature PCC, while the alternating current (ac) magnetic susceptibility in (d) was measured with the mutual induction method in PCC.

Figure 4

Temperature-pressure phase diagram of $\mathrm{Rb}{\mathrm{V}}_3{\mathrm{Sb}}_5$. Pressure dependences of (a) $T^{*}$, (b) $T_{\mathrm{c}}$, and (c) the superconducting transition width $\mathrm{\Delta }{T}_{\mathrm{c}}$ determined from the resistivity and magnetic measurements on several samples, and (d) left shows the zero-temperature upper critical field ${\mu }_0{H}_{\mathrm{c}2}\left(0\right)$ obtained from the empirical Ginzburg-Landau (GL) fitting, and right shows the initial slope of upper critical field ${\mu }_0{H}_{\mathrm{c}2}$ determined from the linear fitting to the data in Figs. 5 and 5.

Figure 5

Temperature dependences of the upper critical field ${\mu }_0{H}_{\mathrm{c}2}$ at different pressures measured with (a) a piston cylinder cell (PCC) and (b) a cubic anvil cell (CAC). The broken lines represent the Ginzburg-Landau (GL) fitting curves.